A366841 Least positive integer whose odd prime factors sum to n, starting with n = 5.

5, 9, 7, 15, 27, 21, 11, 35, 13, 33, 105, 39, 17, 65, 19, 51, 195, 57, 23, 95, 171, 69, 285, 115, 29, 161, 31, 87, 483, 93, 261, 155, 37, 217, 465, 111, 41, 185, 43, 123, 555, 129, 47, 215, 387, 141, 645, 235, 53, 329, 705, 159, 987, 265, 59, 371, 61, 177

Offset: 5

Author

Gus Wiseman, Oct 27 2023

Keywords

• nonn

Comments

All terms are odd.

It seems that all composite terms not divisible by 3 form a supersequence of A292081. - Ivan N. Ianakiev, Oct 30 2023

Examples

			The terms together with their prime factors (which sum to n) begin:
    5 = 5
    9 = 3*3
    7 = 7
   15 = 3*5
   27 = 3*3*3
   21 = 3*7
   11 = 11
   35 = 5*7
   13 = 13
   33 = 3*11
  105 = 3*5*7
		

Links

• Michel Marcus, Table of n, a(n) for n = 5..1000

Crossrefs

This is the odd case of A056240.

Positions of first appearances in A366840 (sum of odd prime factors).

The partition triangle for this statistic is A366851, even A116598.

A001414 adds up prime factors, triangle A331416.

A019507 lists numbers with (even factor sum) = (odd factor sum).

A027746 lists prime factors, length A001222.

A087436 counts odd prime factors, even A007814.

A366528 adds up odd prime indices, triangle A113685 (without zeros A365067).

Cf. A031368, A036349, A056239, A066208, A100005, A112798, A239261, A257991, A335657, A366839.

Programs

Mathematica

nn=1000;
w=Table[Total[Times@@@DeleteCases[If[n==1,{},FactorInteger[n]],{2,_}]],{n,nn}];
spnm[y_]:=Max@@Select[Union[y],Function[i,Union[Select[y,#<=i&]]==Range[i]]];
Table[Position[w,k][[1,1]],{k,5,spnm[Join[{1,2,3,4},Take[w,nn]/.(0->1)]]}]

PARI

f(n) = my(f=factor(n), j=if (n%2, 1, 2)); sum(i=j, #f~, f[i,1]*f[i,2]); \\ A366840
a(n) = my(k=1); while (f(k) != n, k++); k; \\ Michel Marcus, Nov 02 2023